Normal Basis Exhaustive Search: 10 Years Later

  • L. Moura
  • D. Panario
  • D. Thomson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11321)


This paper concerns an exhaustive search for normal bases with minimum complexity in finite fields \(\mathbb {F}_{2^n}\) over \(\mathbb {F}_2\) for \(n \le 46\). This is a followup paper to [11], which appeared one decade ago in 2008 and completed the cases \(n \le 39\). We extend the results in [11] by taking advantage of a combination of algorithmic improvements, more efficient implementations and massive parallelism.


Finite fields Normal bases NTL Parallel computing 



We would like to thank the three reviewers for their helpful suggestions, which greatly improved the presentation of this paper.


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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.University of OttawaOttawaCanada
  2. 2.Carleton UniversityOttawaCanada

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